On Global Dynamics of Schrödinger Map Flows on Hyperbolic Planes Near Harmonic Maps
On Global Dynamics of Schrödinger Map Flows on Hyperbolic Planes Near Harmonic Maps
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DOI：
10.1007/s00220-022-04368-z
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发表时间：
2020-08
影响因子：
2.4
通讯作者：
Ze Li
中科院分区：
文献类型：
--
作者：
Ze Li
The results of this paper are twofold. In the first part, we prove that for Schrödinger map flows from hyperbolic planes to Riemannian surfaces with non-positive sectional curvatures, the harmonic maps which are holomorphic or anti-holomorphic of arbitrary size are asymptotically stable. In the second part, we prove that for Schrödinger map flows from hyperbolic planes into Kähler manifolds, the admissible harmonic maps of small size are asymptotically stable. The asymptotic stability results stated here contain two types: one is the convergence inas the previous works, the other is convergence to harmonic maps plus radiation terms in the energy space, which is new in literature of Schrödinger map flows without symmetric assumptions.
